If $a + b + c = 10$ and $x + y + z = -1$, what is $3a - 7z + 3c - 7y + 3b - 7x$ ?
Solution: $= 3a + 3b + 3c - 7x - 7y - 7z$ $= (3) \cdot (a + b + c) + (-7) \cdot (x + y + z)$ $= (3) \cdot (10) + (-7) \cdot (-1)$ $= 30 + 7$ $= 37$